Circular motion worksheet with answers

Free printable Circular motion worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
r = 0.9 mvmax​ = ?

A 1.7 kg stone is whirled in a horizontal circle of radius 0.9 m on a smooth, level table, held by a string that breaks at a tension of 60 N. Find the highest speed vmax the stone can have.

m = 1.7 kgr = 0.9 mTmax = 60 N
vmax = m/s
2.Easy
r = ?120 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.5 m/s². What is the smallest radius rmin for a curve taken at 120 km/h?

v = 120 km/hamax = 1.5 m/s²
rmin = m
3.Medium
r = 3 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.5. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 3 mμs = 0.5g = 9.81 m/s²
n = rpm
4.Medium
L = 0.9 m50°

A small ball on a string of length 0.9 m moves in a horizontal circle so that the string makes a constant angle of 50° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 0.9 mθ = 50°g = 9.81 m/s²
T = s
5.Hard
r = 0.8 mv = 9 m/s

A 1.9 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 9 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.9 kgr = 0.8 mv = 9 m/sg = 9.81 m/s²
T = N
6.Hard
r = 0.9 mv = ?

A ball on a string 0.9 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed vmin at the top for which the string just stays tight?

r = 0.9 mg = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. vmax = 5.636 m/s
  2. 2. rmin = 740.7 m
  3. 3. n = 24.42 rpm
  4. 4. T = 1.526 s
  5. 5. T = 211 N
  6. 6. vmin = 2.971 m/s

Full step-by-step solutions: practise this topic on examproblems.com.